Scattering-matrix propagation algorithm in full-vectorial optics of multilayer grating structures.

Area of Science:

• Electromagnetics and Optics
• Computational Physics
• Materials Science

Background:

• Analyzing electromagnetic wave scattering from multilayer structures is crucial for optical and electronic device design.
• Existing methods can face stability and convergence issues with increasing structural complexity.

Purpose of the Study:

• To develop a numerically stable symbolic algorithm for electromagnetic plane wave scattering.
• To decouple forward and backward scattered wave amplitudes for improved analysis.
• To provide a robust solution for inhomogeneous multilayer and grating structures.

Main Methods:

• Symbolic formulation of scattering-matrix propagation.
• Development of an algorithm that decouples recurrences for wave amplitudes.
• Fourier-transform discretization for numerical studies of grating structures.

Main Results:

• A stable scattering-matrix solution procedure is established, independent of numerical implementation details.
• The algorithm demonstrates stability against variations in truncation order, layer depth, and layer number.
• Numerical studies confirm the recapitulation of convergence issues for TM polarization in grating structures.

Conclusions:

• The developed scattering-matrix algorithm offers a stable and reliable method for analyzing complex multilayer structures.
• This approach provides a robust framework for studying electromagnetic wave interactions in photonic and electronic devices.
• Further numerical investigations can explore optimizations and applications for specific grating designs.